1. Use the definition of the derivative to find the derivative of the following functions. 1 (b) f(x) = 1 (a) f(x)= Vx +2 (c) f(x) = 3x – - -

Q: 1. Let {an} be a sequence in R with an > 0 and 0 < lim inf→∞ an ≤ lim Supn an < ∞. Prove that 1 lim…

A:

Q: A bin contains 5 red and 5 green balls. 2 balls are chosen at random, without replacement. Let the…

A:

Q: Two manufacturing plants produce similar parts. Plant 1 produces 1,000 parts, 100 of which are…

A: According to the provided information, Plant 2 produces 2000 parts, of which 150 are defective Total…

Q: Let v1 = [1, 1, 0, 2], v2 = [0, 1, 2, 3], v3 = [-1, 0, 2, 1), V4 = [ 3, 1, -4, 0] and b = [4, 3, -2,…

A: Given

Q: Drag and place the numbers to the correct number line. ++++ 43-2 -1 0 1 2 3 4 5 ww +++++ 4 -3 -2 -1…

A: Here, 164, -0.8, 25, 112, -104, 178, -366, -π, -15

Q: Let fn(x) = n²x²(1 – x) on [0, 1]. On what closed subset, F C [0, 1], does the sequence {fn}…

A:

Q: Prove that lim în + lim Yn ≤ lim (xn + Yn) n→∞ n→∞ n→∞ if the left side is not of the form (-∞) +…

A: Solution:  We  have  to  first  recall  the  definition  of limit  inferior. Let  un be a bounded…

Q: Find a counterexample to show that the following statement is false. The sum of two four-digit…

A:

Q: The table below shows the number of accidents, fatalities, hours flown, and miles flown for a…

A: Given: Year Accidents Fatalities Hours Flown (millions) Miles Flown (billions) 2004 49 95…

Q: If sup A < inf B for sets A and B, then there exists a c€R satisfying a <c<b for all a EA and bEB.

A:

Q: Show that for every x E R, there exists an n EN such that <x<n.

A:

Q: Given the following data sets. Data Set I 41 44 45 47 47 48 51 53 58 66 Data Set II 20 37 48 48 49…

A: Data can be raw or grouped, with some pros and cons associated with both of them. The raw data has…

Q: Suppose someone began counting a federal debt of approximately $15 trillion, $3 at a time. If he…

A: Given a federal debt is approx. $15 trillion, and counts $3 each second.  So, No of seconds=Total…

Q: Use the e- 8 property in Definition 19.1 to show that f(x) 1 is uniformly continuous on the interval…

A:

Q: Three people cire Selected from a group of fifteen mean and 8even women. find te followwing…

A: A group consists of 15 men and 7 women, that is totally there are 22 people in the group. From the…

Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

A:

Q: 1) Function f (x) = sinx around point x, = 0 ; a)write the third order Taylor polynomial and the…

A: since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: College students' responses to questions about employment Construct 95% confidence intervals for the…

A: Given data,   n=2500 Construct 95% CI

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

A:

Q: Find the supremum of the set A = { cos (1/n): n E N}, if it does not exist then state so.

A:

Q: A local pawn shop has 10 items for sale. The 23, 28, 41, 51 For the above data, find: a. The range…

A: Hello. Since your question has multiple, we will solve first question for you. If you want remaining…

Q: Identify the minima and maxima of the function. The relative minimum of the function is The absolute…

A: Given: The objective is to find the relative minimum, relative maximum, absolute minimum and…

Q: A simple random sample is one in which ...... O Every unit of the population has an equal chance of…

A: Simple random sampling: In simple random sampling, all units in the population are randomly selected…